In a complex ecohydrologic system, vegetation and soil variables combine to dictate heat fluxes, and these fluxes may vary depending on the extent to which drivers are linearly or nonlinearly interrelated. From a modeling and causality perspective, uncertainty, sensitivity, and performance measures all relate to how information from different sources “flows” through a model to produce a target, or output. We address how model structure, broadly defined as a mapping from inputs to an output, combines with source dependencies to produce a range of information flow pathways from sources to a target. We apply information decomposition, which partitions reductions in uncertainty into synergistic, redundant, and unique information types, to a range of model cases. Toy models show that model structure and source dependencies both restrict the types of interactions that can arise between sources and targets. Regressions based on weather data illustrate how different model structures vary in their sensitivity to source dependencies, thus affecting predictive and functional performance. Finally, we compare the Surface Flux Equilibrium theory, a land-surface model, and neural networks in estimating the Bowen ratio and find that models trade off information types particularly when sources have the highest and lowest dependencies. Overall, this study extends an information theory-based model evaluation framework to incorporate the influence of source dependency on information pathways. This could be applied to explore behavioral ranges for both machine learning and process-based models, and guide model development by highlighting model deficiencies based on information flow pathways that would not be apparent based on existing measures.

中文翻译：

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源关系和模型结构决定了生态水文模型中的信息流路径

在复杂的生态水文系统中，植被和土壤变量共同决定了热通量，这些通量可能会根据驱动因素线性或非线性相关的程度而变化。从建模和因果关系的角度来看，不确定性、敏感性和性能测量都与来自不同来源的信息如何“流动”通过模型以产生目标或输出有关。我们讨论了模型结构（广义地定义为从输入到输出的映射）如何与源依赖关系相结合，以产生从源到目标的一系列信息流路径。我们将信息分解（将不确定性的减少划分为协同、冗余和独特的信息类型）应用于一系列模型案例。玩具模型表明，模型结构和源依赖关系都限制了源和目标之间可能出现的交互类型。基于天气数据的回归说明了不同模型结构对源依赖性的敏感性如何变化，从而影响预测和功能性能。最后，我们比较了地表通量平衡理论、地表模型和神经网络在估计鲍文比率时的情况，发现模型权衡了信息类型，特别是当源具有最高和最低的相关性时。总体而言，本研究扩展了基于信息论的模型评估框架，以纳入源依赖对信息路径的影响。这可以用于探索机器学习和基于过程的模型的行为范围，